# Solved – How to determine which variables are statistically significant in multiple regression

rregressionself-studystatistical significance

From my model, I'm asked to determine which variables are statistically significant.

fitted.model <- lm(spending ~ sex + status + income, data=spending)


My results were as follows:

Coefficients:
Estimate  Std. Error t value   Pr(>|t|)
(Intercept)    22.55565   17.19680   1.312   0.1968
sex         **-22.11833**  8.21111  -2.694   0.0101 *
status          0.05223    0.28111   0.186   0.8535
income          4.96198    1.02539   4.839 1.79e-05 ***
verbal         -2.95949    2.17215  -1.362   0.1803

Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Residual standard error: 22.69 on 42 degrees of freedom
Multiple R-squared: 0.5267, Adjusted R-squared: 0.4816
F-statistic: 11.69 on 4 and 42 DF,  p-value: 1.815e-06.


Question: Do I have to look at the last column? If so, then sex and income would be statistically significant.

Yes, based on the output, sex and income are statistically significant.
sex and possibly status are nominal variables, so it's odd that they appear in the model as is. It could work, if they are 0/1 variables, but it still opens up the potential for error.
To be on the safe side, for sex and any other nominal variable, include it in the model like this: factor(sex):
fitted.model <- lm(spending ~ factor(sex) + status + income, data=spending)